Let a circle centered at $O$ have radius $OA=10$. Let OB be perpendicular on OA.Let G and E be points respectively on on OB and OA.Let F be a point on the circumference such that GFEO is a rectangle.Let us join G and E.If perimeter of GFOE is 24,how can we find the length of GE?
All that I have been able to do is to find out that BG+EA=8.I also tried to calculate BA but that does not seem to take me any closer than I initially was.I am extremely sorry for the lack of work which I have shown.But the original question was posed differently and I believe that this is the final piece of the puzzle.For more info,see Problem-9 of this question.
EDIT: As hhsaffar pointed out in the comment section,GF is the other diagonal of the rectangle.But GF is just a radius of the circle.Therefore,GF=10=GE
Credits to hhsaffar for this solution and Lucian for spotting the lack of relevant information in the original question.
Since $GFOE$ is a rectangle,its diagonals are equal.We are trying to figure out the length of diagonal GE.But since the diagonals are equal, $GE=OF$. But $OF$ is the distance between the center and the circumference of the circle,that is,$OF$ is the radius.But the radius of the circle,as given,is $10$.Therefore $GE=OF=10$, thus ending the solution.